Question: Solve for $x$ and $y$ using elimination. ${2x-4y = -26}$ ${-2x-3y = -44}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $-7y = -70$ $\dfrac{-7y}{{-7}} = \dfrac{-70}{{-7}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {2x-4y = -26}\thinspace$ to find $x$ ${2x - 4}{(10)}{= -26}$ $2x-40 = -26$ $2x-40{+40} = -26{+40}$ $2x = 14$ $\dfrac{2x}{{2}} = \dfrac{14}{{2}}$ ${x = 7}$ You can also plug ${y = 10}$ into $\thinspace {-2x-3y = -44}\thinspace$ and get the same answer for $x$ : ${-2x - 3}{(10)}{= -44}$ ${x = 7}$